Analysis of zz-www.sudokuwiki.org-0134-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=134

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=134

position: ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. initial

Autosolve

position: ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 4,7 => CTR => H1: 3,9
* PRF # B2: 4,7 => SOL
* DIS # C2: 4,7 => CTR => C2: 3,5
* PRF # I4: 4,6 => SOL
* DIS # C5: 4,6 => CTR => C5: 2,3
* DIS # D5: 4,6 => CTR => D5: 1,2,5
* PRF # C8: 5,7 => SOL
* DIS # H9: 5,7 => CTR => H9: 4,8,9
* PRF # I9: 5,7 => SOL
* PRF # C2: 3,4 => SOL
* CNT  10 HDP CHAINS /  33 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # H1: 4,7 => CTR => H1: 3,9
* PRF H1: 3,9 # B2: 4,7 => SOL
* STA H1: 3,9 + B2: 4,7
* CNT   2 HDP CHAINS /   6 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. initial
..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. autosolve
518642937273519468694837521739256814842173659156984372321495786465728193987361245 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
G2: 4,7
G5: 4,6
C9: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,A6: 1.. / B5 = 1  =>  4 pairs (_) / A6 = 1  =>  3 pairs (_)
G8,I9: 1.. / G8 = 1  =>  4 pairs (_) / I9 = 1  => 15 pairs (_)
F9,I9: 1.. / F9 = 1  =>  4 pairs (_) / I9 = 1  => 15 pairs (_)
G1,G8: 1.. / G1 = 1  => 15 pairs (_) / G8 = 1  =>  4 pairs (_)
H3,I3: 2.. / H3 = 2  =>  5 pairs (_) / I3 = 2  =>  3 pairs (_)
B7,C8: 2.. / B7 = 2  =>  0 pairs (*) / C8 = 2  =>  0 pairs (X)
B2,C2: 3.. / B2 = 3  =>  4 pairs (_) / C2 = 3  =>  0 pairs (*)
H1,H3: 3.. / H1 = 3  =>  3 pairs (_) / H3 = 3  =>  0 pairs (X)
A7,B7: 3.. / A7 = 3  =>  4 pairs (_) / B7 = 3  =>  0 pairs (X)
E1,H1: 3.. / E1 = 3  =>  0 pairs (X) / H1 = 3  =>  3 pairs (_)
A4,A7: 3.. / A4 = 3  =>  0 pairs (X) / A7 = 3  =>  4 pairs (_)
C2,C5: 3.. / C2 = 3  =>  0 pairs (*) / C5 = 3  =>  0 pairs (X)
A1,C2: 5.. / A1 = 5  =>  0 pairs (*) / C2 = 5  =>  0 pairs (X)
I4,H5: 5.. / I4 = 5  => 10 pairs (_) / H5 = 5  =>  0 pairs (*)
C2,D2: 5.. / C2 = 5  => 10 pairs (_) / D2 = 5  =>  0 pairs (*)
D5,H5: 5.. / D5 = 5  => 10 pairs (_) / H5 = 5  =>  0 pairs (*)
C8,H8: 5.. / C8 = 5  =>  0 pairs (*) / H8 = 5  =>  0 pairs (X)
A1,A9: 5.. / A1 = 5  =>  0 pairs (*) / A9 = 5  =>  0 pairs (X)
E1,E4: 5.. / E1 = 5  => 10 pairs (_) / E4 = 5  =>  0 pairs (*)
I4,I9: 5.. / I4 = 5  => 10 pairs (_) / I9 = 5  =>  0 pairs (*)
G4,H6: 8.. / G4 = 8  =>  3 pairs (_) / H6 = 8  =>  5 pairs (_)
B7,B9: 8.. / B7 = 8  =>  9 pairs (_) / B9 = 8  =>  3 pairs (_)
D6,E6: 9.. / D6 = 9  =>  3 pairs (_) / E6 = 9  =>  4 pairs (_)
* DURATION: 0:00:31.563370  START: 06:01:42.651367  END: 06:02:14.214737 2017-05-01
* CP COUNT: (23)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G2,G5)
* ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2..
* PAIR G2: 4,7 BLK 3
G1: 4,7,1,9                              # reduction candidate for 4,7
G1: 4,7                                  #  9 pairs
H1: 4,7,3,9                              # reduction candidate for 4,7
H1: 4,7 => CTR
* 548632971273519468.96847532.3925.81.812473659.5419832..21..5...465.2.1.3987361245
H1: 3,9                                  #  4 pairs
I1: 4,7,1                                # reduction candidate for 4,7
I1: 4,7                                  #  7 pairs
H3: 4,7,2,3,9                            # reduction candidate for 4,7
H3: 4,7                                  #  8 pairs
I3: 4,7,1,2                              # reduction candidate for 4,7
I3: 4,7                                  #  9 pairs
* PAIR G2: 4,7 ROW 2
B2: 4,7,3                                # reduction candidate for 4,7
B2: 4,7 => SOLVED
* 518642937273519468694837521739256814842173659156984372321495786465728193987361245
B2: 3                                    #  4 pairs
C2: 4,7,3,5                              # reduction candidate for 4,7
C2: 4,7 => CTR
* 5.8..2...234519768..68..52...9.538128.327..59.52198374321.85...465.2.1.39873.1245
C2: 3,5                                  #  4 pairs
D2: 4,7,5                                # reduction candidate for 4,7
D2: 4,7                                  # 10 pairs
* PAIR G2: 4,7 COL G
G4: 4,7,6,8                              # reduction candidate for 4,7
G4: 4,7                                  #  5 pairs
G7: 4,7,6,8,9                            # reduction candidate for 4,7
G7: 4,7                                  #  5 pairs
* PAIR G5: 4,6 BLK 6
G4: 4,6,7,8                              # reduction candidate for 4,6
G4: 4,6                                  # 11 pairs
I4: 4,6,2,5,7                            # reduction candidate for 4,6
I4: 4,6 => SOLVED
* 518642937273519468694837521739256814842173659156984372321495786465728193987361245
I4: 2,5,7                                #  3 pairs
I6: 4,6,2,7                              # reduction candidate for 4,6
I6: 4,6                                  #  6 pairs
* PAIR G5: 4,6 ROW 5
C5: 4,6,2,3                              # reduction candidate for 4,6
C5: 4,6 => CTR
* 5.8..2...2.3519.68...8..52...9.5..128..27..59.5219.3..321.85...465.27183987361245
C5: 2,3                                  #  4 pairs
D5: 4,6,1,2,5                            # reduction candidate for 4,6
D5: 4,6 => CTR
* 5.86.2..12.3519.681.68.75...3925..1.812473659.5419.3..321..5...465.2.1.3987361245
D5: 1,2,5                                #  3 pairs
F5: 4,6,1,3                              # reduction candidate for 4,6
F5: 4,6                                  #  7 pairs
* PAIR G5: 4,6 COL G
G7: 4,6,7,8,9                            # reduction candidate for 4,6
G7: 4,6                                  #  8 pairs
G7: 7,8,9                                #  3 pairs
* PAIR C9: 5,7 BLK 7
C8: 5,7,2                                # reduction candidate for 5,7
C8: 5,7 => SOLVED
* 518642937273519468694837521739256814842173659156984372321495786465728193987361245
C8: 2                                    # 10 pairs
A9: 5,7,9                                # reduction candidate for 5,7
A9: 5,7                                  # 10 pairs
* PAIR C9: 5,7 ROW 9
H9: 5,7,4,8,9                            # reduction candidate for 5,7
H9: 5,7 => CTR
* 5.8..2...2..519.68...8..5....9.5..1.8...7..59.5....3....1..5...465.....39873..2..
H9: 4,8,9                                #  3 pairs
I9: 5,7,1,4,6                            # reduction candidate for 5,7
I9: 5,7 => SOLVED
* 518642937273519468694837521739256814842173659156984372321495786465728193987361245
I9: 1,4,6                                # 10 pairs
* PAIR C9: 5,7 COL C
C2: 5,7,3,4                              # reduction candidate for 5,7
C2: 3,4 => SOLVED
* 518642937273519468694837521739256814842173659156984372321495786465728193987361245
C2: 5,7                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0134-base-pr-000.dot
* REASONING
* DIS # H1: 4,7 => CTR => H1: 3,9
* PRF # B2: 4,7 => SOL
* DIS # C2: 4,7 => CTR => C2: 3,5
* PRF # I4: 4,6 => SOL
* DIS # C5: 4,6 => CTR => C5: 2,3
* DIS # D5: 4,6 => CTR => D5: 1,2,5
* PRF # C8: 5,7 => SOL
* DIS # H9: 5,7 => CTR => H9: 4,8,9
* PRF # I9: 5,7 => SOL
* PRF # C2: 3,4 => SOL
* CNT  10 HDP CHAINS /  33 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G2,G5)
* ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2..
* PAIR G2: 4,7 BLK 3
G1: 4,7,1,9                              # reduction candidate for 4,7
G1: 4,7                                  #  9 pairs
H1: 4,7,3,9                              # reduction candidate for 4,7
H1: 4,7 => CTR
* 548632971273519468.96847532.3925.81.812473659.5419832..21..5...465.2.1.3987361245
I1: 4,7,1                                # reduction candidate for 4,7
I1: 4,7                                  #  7 pairs
H3: 4,7,2,3,9                            # reduction candidate for 4,7
H3: 4,7                                  #  8 pairs
I3: 4,7,1,2                              # reduction candidate for 4,7
I3: 4,7                                  #  9 pairs
* PAIR G2: 4,7 ROW 2
B2: 4,7,3                                # reduction candidate for 4,7
B2: 4,7 => SOLVED
* 518642937273519468694837521739256814842173659156984372321495786465728193987361245
* DURATION: 0:00:06.126513  START: 06:02:38.988110  END: 06:02:45.114623 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0134-base-pr-001.dot
* REASONING
* DIS # H1: 4,7 => CTR => H1: 3,9
* PRF H1: 3,9 # B2: 4,7 => SOL
* STA H1: 3,9 + B2: 4,7
* CNT   2 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=134

Solution

position: 518642937273519468694837521739256814842173659156984372321495786465728193987361245 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # G1: 4,7 => UNS
* DIS # H1: 4,7 => CTR => H1: 3,9
* INC # H1: 3,9 => UNS
* INC # I1: 4,7 => UNS
* INC # H3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* PRF # B2: 4,7 => SOL
* INC # B2: 3 => UNS
* DIS # C2: 4,7 => CTR => C2: 3,5
* INC # C2: 3,5 => UNS
* INC # D2: 4,7 => UNS
* INC # G4: 4,7 => UNS
* INC # G7: 4,7 => UNS
* INC # G4: 4,6 => UNS
* PRF # I4: 4,6 => SOL
* INC # I4: 2,5,7 => UNS
* INC # I6: 4,6 => UNS
* DIS # C5: 4,6 => CTR => C5: 2,3
* INC # C5: 2,3 => UNS
* DIS # D5: 4,6 => CTR => D5: 1,2,5
* INC # D5: 1,2,5 => UNS
* INC # F5: 4,6 => UNS
* INC # G7: 4,6 => UNS
* INC # G7: 7,8,9 => UNS
* PRF # C8: 5,7 => SOL
* INC # C8: 2 => UNS
* INC # A9: 5,7 => UNS
* DIS # H9: 5,7 => CTR => H9: 4,8,9
* INC # H9: 4,8,9 => UNS
* PRF # I9: 5,7 => SOL
* INC # I9: 1,4,6 => UNS
* INC # C2: 5,7 => UNS
* PRF # C2: 3,4 => SOL
* CNT  33 HDP CHAINS /  33 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G1: 4,7 => UNS
* DIS # H1: 4,7 => CTR => H1: 3,9
* INC H1: 3,9 # I1: 4,7 => UNS
* INC H1: 3,9 # H3: 4,7 => UNS
* INC H1: 3,9 # I3: 4,7 => UNS
* PRF H1: 3,9 # B2: 4,7 => SOL
* STA H1: 3,9 + B2: 4,7
* CNT   6 HDP CHAINS /   6 HYP OPENED